notes06-07-page314 - The flux of material through a plane...

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Unformatted text preview: The flux of material through a plane depends on the concentration difference J = −D dC 1 dn dC =⇒ = −D dx A dt dx where D is the diffusion constant dC 1 dn = −D A dt dx (45.2) This is Fick’s first law of diffusion (in one dimension). The change in concentration in a lamina between x and dx with time is given by the flux in minus the flux out of the lamina: J (x) − J (x + dx) ∂J ∂C = =− ∂t dx ∂x (45.3) Using Fick’s first law for J ∂ ∂C ∂C = D . ∂t ∂x ∂x If D is truly constant we get Fick’s second law of diffusion: ∂ 2C ∂C =D 2. ∂t ∂x (45.4) (45.5) 302 ...
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